Valuations, intersections and Belyi functions--some remarks on the construction of heights
type: Item
instance of: scholarly article
title: Valuations, intersections and Belyi functions--some remarks on the construction of heights
zbMATH Open document ID: 1142.14014
author: Răzvan Liţcanu
published in: Expositiones Mathematicae
publication date: 2007-07-19T00:00:00Z
review text: This note discusses several approaches to defining the height of a smooth projective curve \(X\) defined over a number field \(K\). The definitions discussed include the Néron-Tate height \(\widehat h(X)\) of \(X\) viewed as a subvariety of its Jacobian; the self-intersection of the relative dualizing sheaf with admissible metric; the least upper bound on the set of \(\epsilon>0\) for which the set \(\{P\in X(\overline K):\widehat h(\phi_{D_0}(P))\leq\epsilon\}\) is finite (from the Bogomolov conjecture); and the minimal degree of a ``Belyĭ map'' \(X\to\mathbb P^1\) unramified outside of \(0\), \(1\), and \(\infty\). Comparison theorems are stated, and references are given for the proofs.
reviewed by: Paul Vojta
Mathematics Subject Classification ID: 14G40
Mathematics Subject Classification ID: 14H25
Mathematics Subject Classification ID: 14H30
zbMATH DE Number: 5173104
zbMATH Keywords: Néron-Tate canonical height
zbMATH Keywords: Bogomolov conjecture
zbMATH Keywords: Belyĭ map
MaRDI profile type: Publication
full work available at URL: j.exmath.2006.06.002
OpenAlex ID: W2110739557
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DOI: 10.1016/J.EXMATH.2006.06.002
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